Question

There are 10 students in a classroom, including the triplets Hugh, Stu, and Lou. If 3 of the 10 are randomly selected to give speeches, what is the probability that Hugh will be first, Stu will be second, and Lou will be third?

Answer 1

Answer:

The probability that Hugh will be first, Stu will be second, and Lou will be third is $\frac{1}{720}$.

Step-by-step explanation:

Total number of students in a classroom = 10

Hugh, Stu, and Lou are three student are already included in 10 students.

We need to find the probability that Hugh will be first, Stu will be second, and Lou will be third.

The probability that Hugh will be first = $\frac{1}{10}$

One student is selected, so the number of remaining students is 9.

The probability that Stu will be second = $\frac{1}{9}$

One more student is selected, so the number of remaining students is 8.

The probability that Lou will be third = $\frac{1}{8}$

The probability that Hugh will be first, Stu will be second, and Lou will be third is

$P=\frac{1}{10}\times \frac{1}{9}\times \frac{1}{8}$

$P=\frac{1}{10\times 9\times 8}$

$P=\frac{1}{720}$

Therefore the probability that Hugh will be first, Stu will be second, and Lou will be third is $\frac{1}{720}$.